ISOMETRIC IMMERSIONS IN 3-DIMENSIONAL EUCLIDEAN SPACE
In this paper, we examine the image of geodesic curves of Riemann 2-manifolds under the isometric immersions, in three dimensional Euclidean space. We show that the curvature of these curves is equal to the normal curvature of the manifold in the direction of tangent vector field of the geodesics. Moreover, we prove that if the parameter curves of the manifold are the line of curvature, then the geodesic torsion of geodesics is equal to the torsion of the image curve.
Anahtar Kelimeler:
Immersion, Geodesic, Riemann manifold
ISOMETRIC IMMERSIONS IN 3-DIMENSIONAL EUCLIDEAN SPACE
In this paper, we examine the image of geodesic curves of Riemann 2-manifolds under the isometric immersions, in three dimensional Euclidean space. We show that the curvature of these curves is equal to the normal curvature of the manifold in the direction of tangent vector field of the geodesics. Moreover, we prove that if the parameter curves of the manifold are the line of curvature, then the geodesic torsion of geodesics is equal to the torsion of the image curve.
Keywords:
Immersion, Geodesic, , Riemann manifold,
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- O’Neill B. Elementary Differential Geometry. 2nd ed. New York: Academic Press, 2006.
- Sabuncuoglu A. Diferensiyel Geometri. Ankara: Nobel Yayın Dağıtım, 2006.
- ISSN: 2667-419X
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2010
- Yayıncı: Eskişehir Teknik Üniversitesi
Sayıdaki Diğer Makaleler
ISOMETRIC IMMERSIONS IN 3-DIMENSIONAL EUCLIDEAN SPACE
Recep BAKIŞ, Yıldırım BAYAZIT, Dost Mohammed AHMADY, Saye Nihan ÇABUK